The value of $\cos (52 °) + \cos (68 °) + \cos (172 °)$ is

$0$

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$1$

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$2$

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$\frac{3}{2}$

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Solution

The correct option is A
$0$

Explanation for correct option
Given trigonometric function is $\cos (52 °) + \cos (68 °) + \cos (172 °)$
$\cos (52 °) + \cos (68 °) + \cos (172 °) = \cos (60 ° - 8 °) + \cos (60 ° + 8 °) + \cos (180 ° - 8 °) = 2 \cos (60 °) \cos (8 °) - \cos (8 °) [∵ \cos (A + B) + \cos (A - B) = 2 \cos (A) \cos (B)] = 2 \cdot \frac{1}{2} \cdot \cos (8 °) - \cos (8 °) [∵ \cos (60 °) = \frac{1}{2}] = \cos (8 °) - \cos (8 °) = 0$
Hence the correct option is $Option (A)$

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